On Hodge-Newton Reducible Local Shimura Data of Hodge Type

Citation

Hong, Serin (2018) On Hodge-Newton Reducible Local Shimura Data of Hodge Type. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4F4W-Y024. https://resolver.caltech.edu/CaltechTHESIS:05262018-184212374

Abstract

Rapoport-Zink spaces are formal moduli spaces of p-divisible groups which give rise to local analogues of certain Shimura varieties. In particular, one can construct them from purely group theoretic data called local Shimura data.

The primary purpose of this dissertation is to study Rapoport-Zink spaces whose underlying local Shimura datum is of Hodge type and Hodge-Newton reducible. Our study consists of two main parts: the study of the l-adic cohomology of Rapoport-Zink spaces in relation to the local Langlands correspondence and the study of deformation spaces of p-divisible groups via the local geometry of Rapoport-Zink spaces.

The main result of the first part is a proof of the Harris-Viehmann conjecture in our setting; in particular, we prove that the l-adic cohomology of Rapoport-Zink spaces contains no supercuspidal representations under our assumptions. In the second part, we obtain a generalization of Serre-Tate deformation theory for Shimura varieties of Hodge type.

Thesis Files